Multipliers on fréchet algebra - Azram, Mohammad; Asif, Shehla (2012)
This paper is devoted to establish some fundamentally important results on a commutative semi simple Fréchet algebra. It has been shown that a multiplier on a semi simple Fréchet algebra is a product of an idempotent and an invertible multiplier. It has also been shown that a multiplier on a commutative semi simple Fréchet algebra which is also a Fredholm operator is a product of an idempotent and an invertible element of a continuous linear self mapping of commutative semi simple Fréchet algebra. Finally have shown that for a multiplier T on a commutative semi simple Fréchet algebra A,T2 (A) is closed iff T(A)+ker(T) is closed iff A = T(A)+ker(T) and T is a product of an idempotent and an invertible multiplier iff A = T(A)+ker(T) .